The suggestion, which came on Sunday’s Andrew Marr show, was met with frustration from some in his shadow cabinet, with one member reprimanding Mr Corbyn for floating changes from party policy that had not been agreed.

Some 99.8% per cent of Falkland Islanders who voted in a 2013 referendum on whether to remain an Overseas Territory of the United Kingdom backed keeping the status.

A Number 10 spokesperson said: “The Prime Minister met with the new Argentine President Mauricio Macri. Both agreed that there was an opportunity to embark on a new chapter in relations between our two countries. They covered three areas: economic reform; trade and investment; and the Falkland Islands.

"They discussed how the UK could help with plans to reform the economy in particular on energy, transparency, energy and science.

"On trade and investment the PM stressed that we are keen to significantly expand bilateral trade, which is currently worth around £1.14bn. They agreed that the economic reforms could lead to greater trade opportunities for UK businesses involved in infrastructure, oil & gas, mining and agritech.

"Finally on the Falklands the Prime Minister was clear that our position remained the same and that the recent referendum was absolutely clear on the Islanders wish to remain British."

Discussing the Falklands on Sunday, Mr Corbyn said: “There has to be a discussion about how we can bring about some reasonable accommodation with Argentina.

“It seems to me ridiculous that in the 21st Century we could get into some enormous conflict with Argentina about the islands just off it.

British soldiers during the Falklands War Photo: REX

“Yes, of course the islanders have an enormous say in this; let's bring about some sensible dialogue. It happened before I'm sure it could happen again.”

Mr Corbyn was challenged by a frontbencher over his suggestion that Britain should enter talks with Argentina over the Falklands earlier this week.

Labour sources told The Telegraph that Mr Corbyn was criticised over the interview during a shadow cabinet meeting for floating ideas that were not party policy.